Impact probability computation for NEO resonant returns through a polynomial representation of the Line of Variations

A differential algebra based representation and propagation of the Line of Variations for Near Earth Objects impact monitoring is presented in this paper. The Line of Variations is described at the initial epoch by a high-order polynomial that is propagated forward in time. An Automatic Domain Splitting algorithm is embedded in the numerical integrator, in such a way that when the polynomials truncation error becomes too large, the line is split as many times as necessary to meet accuracy requirements. The Line of Variations is propagated forward in time until an intersection with a properly defined target plane occurs for all the generated subdomains. The subdomains are then projected onto the target plane to compute the impact probability by numerically integrating an associated one-dimensional probability density function. The proposed approach is applied to several test-cases to assess the performance of the method for the different possible shapes of the initial confidence region. Starting from a case of direct encounter, the technique is tested up to the case of a resonant return, which features critical nonlinearities.